Problem: The sum of two numbers is $157$, and their difference is $7$. What are the two numbers?
Answer: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 157}$ ${x-y = 7}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 164 $ $ x = \dfrac{164}{2} $ ${x = 82}$ Now that you know ${x = 82}$ , plug it back into $ {x+y = 157}$ to find $y$ ${(82)}{ + y = 157}$ ${y = 75}$ You can also plug ${x = 82}$ into $ {x-y = 7}$ and get the same answer for $y$ ${(82)}{ - y = 7}$ ${y = 75}$ Therefore, the larger number is $82$, and the smaller number is $75$.